EXPLANATION OF BORON IONIZATIONS
By Prof. L. Kaliambos (Naturel Philosopher in New Energy) April 30, 2015 The electron configuration of ground state gaseous neutral boron is 1s2.2s2. 2p1. However in the absence of a detailed knowledge about the electromagnetic force between the two spinning electrons of opposite spin physicist of the twentieth century under the invalid relativity (EXPERIMENTS REJECT RELATIVITY) using wrong theories could not explain the ground state energy of Boron. Then after my published paper " Spin-spin interactions of electrons and also of nucleons create atomic molecular and nuclear structures" (2008), today it is well known that the Boron electron configuration is given by this correct image with 1s2.2s2. 2p1. Historically despite the enormous success of the Bohr model and the quantum mechanics of Schrodinger in explaining the principal features of the hydrogen spectrum and of other one-electron atomic systems, so far neither was able to provide a satisfactory explanation of ionizations of atoms with many electrons related to the chemical properties of atoms. Though such properties were modified by the periodic table initially proposed by the Russian chemist Mendeleev the reason of this subject of ionizations of elements remained obscure under the influence of the invalid theory of special relativity. (EXPERIMENTS REJECTING EINSTEIN). It is of interest to note that the discovery of the electron spin by Uhlenbeck and Goudsmit (1925) showed that the peripheral velocity of a spinning electron is greater than the speed of light,(FASTER THAN LIGHT), which is responsible for understanding the electromagnetic interaction of two electrons of opposite spin. So it was my paper of 2008, which supplied the clue that resolved this puzzle. According to the “Ionization energies of the elements-WIKIPEDIA” we observe that E1 = 8.298 eV, E2 = 25.15484 eV, E3 = 37.93 eV, E4 = 259.37 eV, and E5 = 340 eV. EXPLANATION OF THE FIRST IONIZATION ENERGY E1 = 8.298 eV = - E(2p1) ' In my paper of 2008 I showed that the shell 2p1 of charge (-e) is screened not only by 1s2 but also by 2s2.( See the paper in “User Kaliambos”). Thus for a perfect screening due to spherical shells we expect to find an effective ζ = 1, because +5e -2e -2e = +1e. Then, under such a theoretical perfect screening the binding energy E(2p1) of the 2p1 electron should be given by E(2p1) = (-13.6) ζ2/ n2 Since ζ =1 and n = 2 one should get E(2p1) = (-13.6) 12/22 = - 3.4 eV. However, in fact, the repulsions of 2p1 with the electrons of both 1s2 and 2s2 lead to the deformation of spherical shells. Under this condition we shall observe an effective ζ > 1. Thus, using the E1 = 8.298 eV = -Ε(2p1) = - (-13.6) ζ2/ 22 One gets ζ2 = 2.44 and ζ = 1.56 >1. '''EXPLANATION OF THE IONIZATION ENERGIES E2 = 25.15484 eV AND E3 = 37.93 eV' For calculating the second ionization energy (E2 = 25.15484 eV) we must start with the third ionization energy E3 = 37.93 eV = - E(2s1) Here E(2s1) is the binding energy of the one electron of B2+ with n = 2 based on the Bohr model. In this case of n = 2 we must find the effective ζ > 3, because the shell 1s2 of the charge (-2e) screens the charge (+5e ) of the nucleus. Of course for a perfect screening due to the spherical shell of 1s2 we should have ζ = 3. Under such a perfect condition we should write E (2s1) = (-13.6) ζ2/22 = (-13.6)32/22 = -30.6 eV However according to the quantum mechanics the 2s1 penetrates the 1s2 which leads to the great deformations of both spherical shells 2s1 and 1s2 . Thus writing E3 = 37.93 eV = - E(2s1) = - (- 13.6)ζ2 / 22 we get ζ2 = 11.156 and ζ = 3.34 >3 . On the other hand for calculating the E2 = 25.15484 eV in my paper (2008) I showed that E2 = 25.15484 eV = - E3 - E(2s2) Under this condition we may write E(2s2) = - E2 - E3 = - 25.15484 - 37.93 = - 63.08 eV Here E(2s2) = - 63.08 eV is the binding energy of the two electrons of 2s2 with opposite spin based on my formula of 2008 as E(2s2) = [ (-27.2)ζ2 + (16.95)ζ - 4.1] / n2 According to the quantum mechanics the two electrons of opposite spin (2s2) penetrate the 1s2 shell. Thus it leads to greater deformations of both 1s2 and 2s2 spherical shells giving an effective ζ > 3, because the charge (-e) of the two electrons of 1s2 screens the charge (+5) of nucleus. Since n = 2 we may write E(2s2) = + (16.95)ζ - 4.1/22 = - 63.08 eV Therefore (27.2ζ2 - 16.95ζ + 4.1) / 22 - 63.08 = 0 Or 6.8ζ2 - 4.24ζ - 62 = 0 Then solving for ζ we get ζ = 3.34. In other words we observe that the repulsions 1s2-2s1 and 1s2-2s2 give the same effective ζ = 3.34 > 3. EXPLANATION OF Ε4 = 259.375 eV AND E5 = 340 '''eV''' Of course the ionization energy E5 = 340 eV = - E(1s1) is due to the one remaining electron of 1s1 with n = 1 given by applying the simple Bohr model for Z = 5 as E5 = - (-13.6)Z2 /12 = - (-13.6)52 = 340 eV. Moreover for calculating the E4 = 259.37 eV I showed in my paper (2008) that the forth ionization energy E4 is given by E4 = E( 1s1) - E(1s2 ) = (-13.6) Z2 - [ (-27.2)Z2 +(16.95)Z - 4.1] Since Z = 5 one gets E4 = (-13.6)52 + (27.2)52 - (16.95)5 + 4.1 = 259.37 eV. It is of interest to note that the E(1s2) and the E(2s2) of two spinning electrons of opposite spin with n =1 and n = 2 respectively are given by applying my formula of my paper of 2008. However In the absence of a detailed knowledge about the electromagnetic force between the two spinning electrons of opposite spin physicists today using wrong theories cannot explain these ionization energies. For example under wrong theories based on qualitative approaches many physicists believe incorrectly that the second electron of the 1s2 shell is less tightly bound because it could be interpreted as a shielding effect; the other electron partly shields the second electron from the full charge of the nucleus. Another wrong way to view the energy is to say that the repulsion of the electrons contributes a positive potential energy which partially offsets the negative potential energy contributed by the attractive electric force of the nuclear charge. Under such false ideas I published my paper of 2008. The first few two-electron atoms are: Z =1 : H- hydrogen anion. Z = 2 : He helium atom. Z = 3 : Li+ lithium atom anion. Z = 4 : Be2+ beryllium ion. Z = 5 : B3+ boron. Prior to the development of quantum mechanics, an atom with many electrons was portrayed like the solar system, with the electrons representing the planets circulating about the nuclear “sun”. In the solar system, the gravitational interaction between planets is quite small compared with that between any planet and the very massive sun; interplanetary interactions can, therefore, be treated as small perturbations. However, In the helium atom with two electrons, the interaction energy between the two spinning electrons and between an electron and the nucleus are almost of the same magnitude, and a perturbation approach is inapplicable. In 1925 the two young Dutch physicists Uhlenbeck and Goudsmit discovered the electron spin according to which the peripheral velocity of a spinning electron is greater than the speed of light. Since this discovery invalidates Einstein’s relativity it met much opposition by physicists including Pauli. Under the influence of Einstein’s invalid relativity physicists believed that in nature cannot exist velocities faster than the speed of light. So, great physicists like Pauli, Heisenberg, and Dirac abandoned the natural laws of electromagnetism in favor of wrong theories including qualitative approaches under an idea of symmetry properties between the two electrons of opposite spin which lead to many complications. Thus in the “Helium atom-Wikipedia” one reads: “Unlike for hydrogen a closed form solution to the Schrodinger equation for the helium atom has not been found. However various approximations such as the Hartree-Fock method ,can be used to estimate the ground state energy and wave function of atoms”. It is of interest to note that in 1993 in Olympia of Greece I presented at the international conference “Frontiers of fundamental physics” my paper “Impact of Maxwell’s equation of displacement current on electromagnetic laws and comparison of the Maxwellian waves with our model of dipolic particles ". The conference was organized by the natural philosophers M. Barone and F. Selleri who awarded me an award including a disc of the atomic philosopher Democritus, because in that paper I showed that LAWS AND EXPERIMENTS INVALIDATE FIELDS AND RELATIVITY . At the same period I tried to find not only the nuclear force and structure but also the coupling of two electrons under the application of the abandoned electromagnetic laws. For example in the well known photoelectric effect the absorption of light contributed not only to the increase of the electron energy but also to the increase of the electron mass, because the particles of light have mass m = hν/c2 .( See my DISCOVERY OF PHOTON MASS ). However the electron spin which gives a peripheral velocity greater than the speed of light cannot be affected by the photon absorption. Thus after 10 years I published my paper “Nuclear structure is governed by the fundamental laws of electromagnetism"(2003) in which I showed not only my DISCOVERY OF NUCLEAR FORCE AND STRUCTURE but also that the peripheral velocity (u >> c) of two spinning electrons with opposite spin gives an attractive magnetic force (Fm) stronger than the electric repulsion (Fe), when the two electrons of mass m and charge (-e) are at a very short separation r < 578.8 /1015 m. Because of the antiparallel spin along the radial direction the interaction of the electron charges gives an electromagnetic force Fem = Fe - Fm . Therefore in my research the integration for calculating the mutual Fem led to the following relation: Fem = Fe - Fm = Ke2/r2 - (Ke2/r4)(9h2/16π2m2c2) Of course for Fe = Fm one gets the equilibrium separation ro = 3h/4πmc = 578.8/1015 m. That is, for r < 578.8/1015 m the two electrons of opposite spin exert an attractive electromagnetic force, because the attractive Fm is stronger than the repulsive Fe . Here Fm is a spin-dependent force of short range. As a consequence this situation provides the physical basis for understanding the pairing of two electrons described qualitatively by the Pauli principle, which cannot be applied in the simplest case of the deuteron in nuclear physics, because the binding energy between the two spinning nucleons occurs when the spin is not opposite (S=0) but parallel (S=1). According to the experiments in the case of two electrons with antiparallel spin the presence of a very strong external magnetic field gives parallel spin (S=1) with electric andmagnetic repulsions given by Fem = Fe + Fm So, according to the well-established laws of electromagnetism after a detailed analysis of paired electrons in two-electron atoms I concluded that at r < 578.8/1015 m a motional EMF produces vibrations of paired electrons. Unfortunately today many physicists in the absence of a detailed knowledge believe that the two electrons of two-electron atoms under the Coulomb repulsion between the electrons move not together as one particle but as separated particles possessing the two opposite points of the diameter of the orbit around the nucleus. In fact, the two electrons of opposite spin behave like one particle circulating about the nucleus under the rules of quantum mechanics forming two-electron orbitals in helium, beryllium etc. In my paper ( 2008) I showed that the positive vibration energy (Ev) described in eV depends on the Ze charge of nucleus as Ev = 16.95Z - 4.1 Of course in the absence of such a vibration energy Ev it is well-known that the ground state energy E described in eV for two orbiting electrons could be given by the Bohr model as E = (-27.2) Z2. So the combination of the energies of the Bohr model and the vibration energies due to the opposite spin of two electrons led to my discovery of the ground state energy of two-electron atoms given by E = (-27.2) Z2 + (16.95 )Z - 4.1 For example the laboratory measurement of the ionization energy of H- yields an energy of the ground state E = - 14.35 eV. In this case since Z = 1 we get E -27.2 + 16.95 - 4.1 = -14.35 eV. In the same way writing for the helium Z = 2 we get E = - 108.8 + 32.9 - 4.1 = -79.0 eV which is equal to the laboratory measurement. In the same way we can calculate the ground state energies for the Z = 3 : Li+ ion , Z = 4 : Be2+ beryllium ion, and Z = 5 : B3+ boron. The discovery of this simple formula based on the well-established laws of electromagnetism was the first fundamental equation for understanding the energies of many-electron atoms, while various theories based on qualitative symmetry properties lead to complications. Category:Fundamental physics concepts